Rotor blades or airfoils are used in many devices with several examples including axial compressors, turbines, engines, or other turbo machinery. For example, an axial compressor has one or more rotors having a series of stages with each stage comprising a row of rotor blades or airfoils followed by a row of static blades or static airfoils. Accordingly, each stage comprises a pair of rotor blades or airfoils and static airfoils. Typically, the rotor blades or airfoils increase the kinetic energy of a fluid that enters the axial compressor through an inlet. Furthermore, the static blades or static airfoils generally convert the increased kinetic energy of the fluid into static pressure through diffusion. Accordingly, the rotor blades or airfoils and static airfoils increase the pressure of the fluid.
During operation, the rotor blades generally vibrate at synchronous and asynchronous frequencies. For example, while the rotor blades may generally vibrate at the synchronous frequencies due to the rotor speed/frequency, the rotor blades may vibrate at the asynchronous frequencies due to aerodynamic instabilities, such as, rotating stall and flutter. The rotor blades have a natural tendency to vibrate at larger amplitudes at certain synchronous frequencies of the rotor blades. Such synchronous frequencies are referred to as resonant frequencies of the rotor blades. The synchronous frequencies of the rotor blades are typically activated at fixed rotor speeds of the rotors. Furthermore, the activation of the resonant frequencies may increase the amplitudes of vibration of the rotor blades. Such increased amplitudes of vibration may damage the rotor blades or lead to cracks in the rotor blades.
The rotor blades operate for long hours under extreme and varied operating conditions, such as, high speed, pressure, and temperature that affect the health of the airfoils. In addition to the extreme and varied operating conditions, certain other factors lead to fatigue and stress of the airfoils. The factors, for example, may include inertial forces including centrifugal force, pressure, resonant frequencies of the airfoils, vibrations in the airfoils, vibratory stresses, temperature stresses, reseating of the airfoils, load of the gas or other fluid, or the like. A prolonged increase in stress and fatigue over a period of time damages the rotor blades resulting in defects or cracks in the rotor blades. Such defects, damages, or cracks in the rotor blades may vary the rotor speeds that activate the rotor blades' resonant frequencies. For example, in a healthy rotor blade if resonant frequencies are activated at a rotor speed R, then when the rotor blade has a crack, the resonant frequencies may get activated at a rotor speed of R±r. These variations in rotor speeds that activate the rotor blades' resonant frequencies may, therefore, be useful in monitoring the health of rotor blades.
Accordingly, it is desirable to determine rotor speeds that activate resonant frequencies of healthy rotor blades. Furthermore it is desirable to determine existence of variations in the rotor speeds that activate resonant frequencies to monitor and assess the health of the rotor blades.